Robot manipulators are complex machines that require precise control. Understanding their dynamics and kinematics is crucial for effective operation. This includes forward and inverse kinematics, velocity kinematics, and dynamics modeling using methods like Lagrangian or Newton-Euler formulations.

Adaptive control techniques help robots handle varying conditions. Methods like Model Reference Adaptive Control and Self-Tuning Regulators adjust controller parameters on the fly. Advanced techniques like force control and performance evaluation ensure robots can interact safely with their environment and operate efficiently.

Robot Manipulator Dynamics and Control

Dynamics and kinematics of manipulators

• Forward kinematics maps joint angles to end-effector position using DH parameters and homogeneous transformation matrices
• Inverse kinematics determines joint angles for desired end-effector position through analytical or numerical methods (Newton-Raphson)
• Velocity kinematics relates joint velocities to end-effector velocity using Jacobian matrix identifies singularities
• Dynamics modeling derives equations of motion via Lagrangian or Newton-Euler formulations
• Equations of motion include inertia matrix, Coriolis and centrifugal terms, and gravity terms
• Actuator dynamics consider motor characteristics and gear transmission effects

Adaptive control for varying conditions

• Model reference adaptive control (MRAC) uses reference model and adaptation laws to adjust controller parameters
• Self-tuning regulators (STR) employ parameter estimation techniques and control law design for online adaptation
• Adaptive computed torque control performs online parameter estimation and adaptive feedforward compensation
• Robust adaptive control incorporates sliding mode control or $H_\infty$ control for improved robustness
• Payload estimation techniques utilize recursive least squares (RLS) or Kalman filtering for real-time mass estimation

Advanced Control Techniques and Performance Evaluation

Force control in environmental contact

• Impedance control defines desired impedance model and uses force feedback for compliant interaction
• Admittance control specifies desired admittance model and utilizes position/velocity feedback
• Hybrid position/force control employs task frame formulation to separate force and position subspaces
• Stiffness control manipulates Cartesian stiffness matrix and joint space stiffness for desired behavior
• Contact modeling considers rigid body contact or compliant contact models for accurate interaction simulation

Performance evaluation of adaptive algorithms

• Performance metrics assess tracking error, settling time, and overshoot
• Stability analysis applies Lyapunov stability theory and input-to-state stability concepts
• Robustness analysis examines controller behavior under parameter variations and external disturbances
• Simulation tools like MATLAB/Simulink and ROS/Gazebo enable virtual testing and validation
• Experimental setup integrates sensors (encoders, force/torque sensors) and implements real-time control
• Comparative analysis evaluates adaptive vs. non-adaptive control and different adaptive control schemes